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Theorem riotaclbg 6360
 Description: Closure of restricted iota. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 24-Dec-2016.)
Assertion
Ref Expression
riotaclbg
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem riotaclbg
StepHypRef Expression
1 riotacl 6335 . 2
2 undefnel2 6318 . . . 4
3 riotaund 6357 . . . . . 6
43eleq1d 2362 . . . . 5
54notbid 285 . . . 4
62, 5syl5ibrcom 213 . . 3
76con4d 97 . 2
81, 7impbid2 195 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wcel 1696  wreu 2558  cfv 5271  cund 6312  crio 6313 This theorem is referenced by:  riotaclb  6361  riotasvd  6363  riotasvdOLD  6364  spwex  14354  supdef  25365 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pow 4204  ax-pr 4230  ax-un 4528 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-nel 2462  df-ral 2561  df-rex 2562  df-reu 2563  df-rab 2565  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-pw 3640  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-opab 4094  df-mpt 4095  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-iota 5235  df-fun 5273  df-fv 5279  df-undef 6314  df-riota 6320
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